About one method of extension operator construction
E. M. Popova · Science and Education of the Bauman MSTU · 2014
This article examines S.L. Sobolev anisotropic spaces. It proposes a method to construct the operator extension T from the banach space of functions to Sobolev anisotropic space. The operator T is the best one in terms of growth rate of high order derivatives from extension function, and its construction is based on any extension operator Ext. The construction method is to apply the approximation operator saving boundary values to the operator Ext. V.I. Burenkov offers this method in the isotropic case while E.M. Popova’s proposal is to use it in the anisotropic one.